Self-optimizing distributed antenna system using soft frequency reuse

ABSTRACT

A method of determining a carrier power in a communications system including a processor includes a) setting a power differential between a reference carrier and one or more carriers, b) measuring a number of satisfied users at the power differential, and c) measuring a capacity for the satisfied users at the power differential. The method also includes d) increasing the power differential by a predetermined amount and e) determining, using the processor, that the number of satisfied users at the increased power differential is greater than or equal to the number of satisfied users at the power differential. The method further includes f) repeating a)-c) and g) setting the carrier power at an iterated power level.

CROSS-REFERENCES TO RELATED APPLICATIONS

This application claims priority to U.S. Provisional Patent ApplicationNo. 61/669,572, filed on Jul. 9, 2012, entitled “Self-OptimizingDistributed Antenna System Using Soft Frequency Reuse,” the disclosureof which is hereby incorporated by reference in its entirety for allpurposes.

SUMMARY OF THE INVENTION

According to an embodiment of the present invention, a method ofdetermining a carrier power in a communications system including aprocessor is provided. The method includes a) setting a powerdifferential between a reference carrier and one or more carriers, b)measuring a number of satisfied users at the power differential, and c)measuring a capacity for the satisfied users at the power differential,which may be referred to as an initial power differential. The methodalso includes d) adjusting the power differential by a predeterminedamount and e) determining, using the processor, that the number ofsatisfied users at the adjusted power differential is greater than orequal to the number of satisfied users at the initial powerdifferential. The method further includes f) repeating a)-e) and g)setting the carrier power at an iterated power level.

As described herein, unbalanced traffic distributions inside cellularnetworks are common occurrences. Embodiments of the present inventionprovide a throughput-balancing system that optimizes cellularperformance according to the geographic traffic distribution in order toprovide a high quality of service (QoS). The throughput of an OrthogonalFrequency Division Multiple Access (OFDMA) based architecture (DAS-SFR)that utilizes a combination Soft Frequency Reuse (SFR) technique and aDistributed Antenna System (DAS) is analyzed in light of embodiments ofthe present invention. A concept employed by this architecture is todistribute the antennas in a hexagonal cell in such a way that thecentral antenna is responsible for serving a special area, using all ofthe frequency bands, while the remaining antennas utilize only a subsetof the frequency bands based on a frequency reuse factor. A DAS-SFR hasthe ability to distribute the cellular capacity (throughput) over agiven geographic area. To enable throughput balancing among DistributedAntennas (DAs), embodiments of the present invention dynamically changethe DA's carrier power to manage the inter-cell interference, as afunction of the time-varying traffic. A Downlink Power Self-Optimization(PSO) algorithm, for three different resource allocation scenarios, isdescribed for the DAS-SFR system. The transmit powers are optimized inorder to maximize the spectral efficiency of a DAS-SFR and maximize thenumber of satisfied users under different user distributions in someembodiments. The PSO algorithm is able to guarantee a high Quality ofService (QoS) that concentrates on the number of satisfied users as wellas the capacity of satisfied users as the two Key Performance Indicators(KPIs). Analytical derivations and simulations are discussed and used toevaluate the system performance for different traffic scenarios, and theresults are presented.

Embodiments of the present invention provide a method and system foradjusting and potentially optimizing the powers of multiple carriers ina DAS-SFR system. By adjusting the power associated with the carriersprovided by the central antenna of each cell, the SFR system enableshigher system performance and an improved user experience as a result ofhigher system bandwidth.

Numerous benefits are achieved by way of the present invention overconventional techniques. For instance, embodiments of the presentinvention control the amount of resources allocated to users located indifferent areas, thereby increasing the frequency efficiency and alsoimproving the data rate for cell edge users. As another example,embodiments of the present invention are useful in adjusting the powersof carriers to increase or maximize Key Performance Indicators, whichare related to Quality of Service. These and other embodiments of theinvention along with many of its advantages and features are describedin more detail in conjunction with the text below and attached figures.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates band width allocation to antennas for three differentcombinations of DAS with SFR, HFR and FFR according to embodiments ofthe present invention;

FIG. 2 illustrates the structure of a Distributed Antenna Systemaccording to an embodiment of the present invention;

FIG. 3 illustrates a block diagram of the Received Signals withInterference Signals and Noises according to an embodiment of thepresent invention;

FIG. 4 is a simplified flowchart illustrating the PSO algorithmaccording to an embodiment of the present invention;

FIG. 5 illustrates plots of ergodic capacity versus the normalizeddistance from the DRU0 according to embodiments of the presentinvention;

FIG. 6 illustrates KPIs versus the ΔP for different distribution usersscheme where C_(th)=0.01W_(RB) according to embodiments of the presentinvention; and

FIG. 7 illustrates KPIs versus the ΔP for different distribution usersscheme where C_(th)=0.07W_(RB) according to embodiments of the presentinvention.

DETAILED DESCRIPTION OF SPECIFIC EMBODIMENTS

In existing networks, parameters are manually adjusted to obtain a highlevel of network operational performance. 3GPP LTE is the preferredcandidate for the next generation wireless networks. In the last 15years, there has been substantial growth in cellular mobilecommunication systems. It is imperative to provide a high quality ofservice (QoS) at a minimum cost. With the substantial increase incellular users, unbalanced throughput distributions are common inwireless networks which decrease the number of satisfied users. Astraffic environments change, the network performance will not beoptimum. Therefore, it is necessary to perform inter-cell optimizationof the network dynamically according to the traffic environment,especially when cell traffic is not uniformly distributed. This is oneof the important optimization issues in self-organizing networks (SON)for 3GPP LTE.

In SON, parameter tuning is done automatically based on measurements.The use of throughput-balancing is meant to deliver extra gain in termsof network performance. For throughput-balancing this is achieved byadjusting the network control parameters in such a way that ultra-highthroughput users can offload to ultra-low throughput users inside thecell. In a live network, high throughput fluctuations occur. A SONenabled network, where the proposed SON algorithm monitors the networkand reacts to these changes in throughput, can achieve betterperformance by distributing the throughput among users.

When the traffic loads among cells are not balanced, the satisfactionprobability of heavily loaded cells may be lower, since theirneighboring cells cause high inter-cell interference on cell edge users.In this case, throughput balancing can be conducted to alleviate andeven avoid this problem.

Inter-cell interference, experienced by cell-edge users, is very highwhen this interference is a result of using the same subcarriers in theadjacent cell in the same time slot. High inter-cell interference meanssevere degradation of the cell-edge throughput since Mobile 3GPP LTEadopts a frequency reuse factor of one which is called Full FrequencyReuse (FFR), in which each cell serves users using the entire systembandwidth.

To mitigate the inter-cell interference in cellular systems, severaltechniques have been incorporated in these standards. Advanced receivertechniques such as Maximum Likelihood (ML) Multiuser Detection (MUD),the MMSE Receiver MUD and Other-cell interference cancellation are thethree potential ways to reduce interference in cellular systems;however, these require a more complicated receiver. Advanced transmittertechniques such as Cooperative Encoding (CA), Closed-Loop MIMO DiversitySchemes (CLMD) and Beam forming are three other techniques to overcomethe interference problem in cellular systems but CA requires veryaccurate channel state knowledge and real time inter-cell coordination,CLMD and Beam forming sacrifice spatial dimensions and require channelstate knowledge.

One possible strategy to alleviate interference, both in the uplink andthe downlink of cellular networks, is to reduce the overall transmitpower by using a Distributed Antenna Systems (DAS), which also has theadditional advantage of improving capacity and coverage.

The other possible strategy is a Soft Frequency Reuse technique; thistechnique effectively reduces the inter-cell interference bygeographically spacing the competing transmissions farther apart, whichbenefits users near the cell boundaries.

A. Distributed Antenna System (DAS):

Distributed antenna systems (DAS) have been widely implemented instate-of-the art cellular communication systems to cover dead spots inwireless communications systems.

A DAS breaks the traditional radio base station architecture into twopieces: a central processing facility and a set of distributed antenna(DA), connected to the central facility by a high-bandwidth network. TheDAS network transports radio signals, in either analog or digital form,to/from the central facility where all the base station's processing isperformed. By replacing a single high-power antenna with severallow-power antennas, distributed to give the same coverage as the singleantenna, a DAS is able to provide more-reliable wireless services withina geographic area or structure while reducing its power consumption.

DAS has the following potential advantages such as: throughputimprovement, coverage improvement, increased cellphone battery life anda reduction in transmitter power. Recent research has shown the benefitsof using DAS in a cellular system for extending coverage, reducing callblocking rate and reducing inter-cell interference. An extension to atraditional DAS system is an Intelligent DAS, wherein each remote hasthe added flexibility of independently transmitting preselectedcarriers.

Most of the research on DAS has focused on investigating SINR advantagesof DAS and analyzing its performance. Some research on DAS has focusedon the analysis of the uplink performance due to its analyticalsimplicity, while there are few studies on the downlink performance ofDAS, although the demand for high-speed data rate will be dominant inthe downlink path. There is also very little research that considers theadvantages of DAS in a multi-cell context.

B. Soft Frequency Reuse (SFR) Technique:

SFR has been proposed as an inter-cell interference mitigation techniquein OFDMA based wireless networks. In SFR, the frequency band is dividedinto a fixed number of sub-bands; all sub-bands are used by all eNBs toserve “near” users; the other sub-bands are dedicated to “far” users.All sub-bands are allocated to the cells according to some predefinedreuse factor. The SFR assigns sub-bands limited amount of transmit powerto reduce inter-cell interference. The transmit power needs to bereduced enough to provide the required throughput to cell edge users ofneighboring cells. Also, the sub-bands of reduced transmit power areused for the inner cell users.

Hard Frequency Reuse (HFR) suffers from a reduced spectral efficiency insuch a way that, in HFR, the frequency band is divided into a fixednumber of sub-bands that are allocated to the cells according to somepredefined reuse factor and lets neighboring cells transmit on differentsub-bands. On the other hand, SFR has the benefit of a full spectralefficiency and is a strong mechanism for inter-cell interferencemitigation.

The capacity of the SFR was evaluated in assuming the offset in thetransmit powers of different sub-bands. Self-organization of thetransmit power in the uncoordinated systems was illustrated in wheresome transient time is required to converge on the equilibrium state ofpower allocation. Recent research on SFR has focused on optimal systemdesign utilizing advanced techniques such as graph theory and convexoptimization to maximize network throughput. Additional work on FFR andSFR consider alternative schedulers and the authors determined thefrequency partitions in a two-stage heuristic approach.

Accordingly, this paper proposes a new architecture to suppressinter-cell interference. The proposed architecture combines DAS and SFRfor an OFDMA system (e.g. LTE). We analyze the potential gains ofDAS-SFR in a multi-cell environment.

The proposed architecture divides the entire spectral bandwidth F into 3parts (F₁, F₂, F₃). The system assigns the eNB the full-reused frequency(all 3 parts) to the central antenna and the other 6 edge antennas workonly on 1 part based on a reuse factor of Δ (ie. Δ=3) in such a way thatneighbor cell edge antennas do not use the same frequency, FIG. 1(a).Two other combinations of DAS with HFR and FFR are also demonstrated inFIG. 1(b) and FIG. 1(c), respectively.

In order to attain user satisfaction, a minimum throughput should beprovided for all users. In this publication, the system QoS is afunction of the number of satisfied users. For a DAS-SFR architecture,the cell-edge throughput can be improved due to the reduced inter-cellinterference as well as from the boosted cell-center transmission power.However, as compared to FFR the overall network throughput decreases atthe same time, since the improvement is obtained at the cost of thecell-center user throughput. Thus, an efficient resource allocation andpower allocation scheme is required to achieve the optimum overallnetwork throughput in the DAS-SFR implementation.

Therefore, to improve the throughput for the cell edge users and furtherincrease the number of satisfied users (the users that can achieve atargeted service bitrate), a downlink Power Self-Optimization (PSO)algorithm for three different resource allocation scenarios is proposedfor the DAS-SFR. The transmit powers are allocated so that the spectralefficiency is maximized for the DAS-SFR, and the number of satisfiedusers is also maximized. The spectral efficiency represented by theergodic capacity is obtained for the different scenarios. The resultsshow that a DAS-SFR architecture effectively addresses inter-cellinterference in a multi-cell environment, especially at the cellboundaries when compared to a HFR cellular architecture. The resultsalso show that a DAS-SFR architecture achieves a non-trivial capacityenhancement over a HFR cellular architecture for a frequency reusefactor of 3.

A contribution of this work is the development of an analyticalframework to evaluate the ergodic capacity of a DAS-SFR architecture.This is an important metric to consider, especially for users at thecell-edge since modern cellular networks are increasingly required toprovide users with high data-rate and a guaranteed quality-of-service(QoS). This work presents a strategy for optimally allocating frequencyRBs to edge users in a DAS-SFR architecture, based on a chosenperformance threshold, which we define as T_(p).

A system model is presented in section II. In section III, theachievable capacity is derived for a distributed antenna system.Formulation of the Power allocation algorithm is discussed in sectionIV. Analytical and simulation results are shown in section V and aconclusion is provided in section VI.

II. System Model

A. System Architecture:

The general architecture of an intelligent DAS in a multi-cellenvironment is shown in FIG. 2, where 7 Digital Remote Units (DRUs) areconnected to an eNB via an optical fiber and a Digital Access Unit(DAU). The DAUs are interconnected and connected to multiple sectors.This capability enables the virtualization of the eNB resources at theindependent DRUs. The eNBs are linked to a public switched telephonenetwork or a mobile switching center. DRUs are sectorized in such a waythat each DRU allocated to a given eNB sector can be simulcast. For thesimulcasting operation, the access network between each eNB and its DRUsshould have a multi-drop bus topology. In contrast, the same area (7DRUs) is covered by a single high-power eNB in a traditional cellularsystem.

The total transmit power of the n-th DRU of i-th cell in f-th frequencypart is denoted P_(n) ^((i,f)), where the central DRU of each cell isindex by n=0.

We also consider the 2-tier cellular structure, where two continuoustiers of eighteen cells surround a given cell. Although this assumptionof only 2-tiers of interfering cells is optimistic, a pessimisticassumption that all the DRUs and the eNB are transmitting full power allthe time easily compensates.

B. Resource Allocation Scenarios:

In a multiuser DAS-SFR system, different users are located at varyingdistances from the DRUs and have varying channel conditions on thesubcarriers. Therefore, resource allocation allows for efficientexploitation of multiuser diversity in the system [20].

Much of the research on SFR system design has focused on how todetermine the size of the frequency partitions [21], for example, in atypical LTE system with a bandwidth of 5 MHz, 25 RBs may be available toserve users for each frequency part (F_(i), i=1, 2, 3) [22].

For a typical central cell, we can assume that the center DRU isassigned to the full-reused frequency and the other six edge DRUs areassigned to F₁. Now, we consider three resource allocation scenarios:

-   -   Scenario 1: F₁, F₂, F₃ RBs are assigned to all users in the        cell. Note that in this scenario, the very low SINR exterior        users are inefficiently using the F₂ and F₃ RBs.    -   Scenario 2: F₁ RBs are assigned to all users but F₂ and F₃ RBs        are solely assigned to interior users. Note that in this        scenario, the available RBs are fully assigned to the interior        users, which leads to a big gap between the numbers of allocated        RBs to the interior users as compared to the exterior users.    -   Scenario 3: F₁ RBs are solely assigned to the exterior users,        whereas the F₂ and F₃ RBs are assigned to the interior users. In        this scenario, all RBs are more fairly assigned between all        users, as compared to the previously mentioned scenario.        Moreover, in this scenario the RBs are allocated to the users        following a SINR-based approach, in which the edge users using        the F₁ RBs, and the interior users using the F₂ and F₃ RBs have        a high SINR.

We primarily assume a single user scenario, and further extend it to auniformly distributed multiuser LTE system. In a multiuser scenario, weinvestigate both the analytical and the simulation results in order toverify the system's capacity improvement.

Received Signal and Channel Model

The downlink path of a DAS can be considered as an equivalent MIMOsystem with additive interference and noise (FIG. 3). The receivedsignal vector of the user in the central cell at frequency f can beexpressed as,

$\begin{matrix}\begin{matrix}{y^{({0,f})} = {{signal} + {interference} + {noise}}} \\{= {{H^{({0,f})}x^{({0,f})}} + {\sum\limits_{i = 1}^{18}{H^{({i,f})}x^{({i,f})}}} + n^{(f)}}}\end{matrix} & (1)\end{matrix}$where H^((i,f))εC^(1×7), i=0, 1, . . . , 18, denotes the channel matrixbetween the DRUs in the i-th cell and the user in the central cell,x^((i,f))=[x₀ ^((i,f)), x₁ ^((i,f)), . . . , x₆ ^((i,f))]^(T)εC^(7×1),i=0, 1, . . . , 18 is the transmitted signal vector of the DRUs in thei-th cell, n^((f))εC^(1×1) denotes the white noise vector withdistribution CN(0, σ_(n) _((f)) ²I₁). The distributed antenna powerconstraint is considered, we haveE[|x _(n) ^((i,f))|² ]≦P _(n) ^((i,f)) , n=0, 1, . . . , 6, i=0, 1, . .. , 18,  (2)where in DAS-SFR,x_(n) ^((i,F) ¹ ⁾=0,P_(n) ^((i,F) ¹ ⁾=0 when (n=1, 2, . . . , 6 and i=1,2, . . . , 7, 9, 11, 13, 15, 17),x_(n) ^((i,F) ² ⁾=0,P_(n) ^((i,F) ² ⁾=0 when (n=1, 2, . . . , 6 and i=0,2, 4, 6, 7, 8, 10, 11, 12, 14, 15, 16, 18),x_(n) ^((i,F) ³ ⁾=0,P_(n) ^((i,F) ³ ⁾=0 when (n=1, 2, . . . , 6 and i=0,1, 3, 5, 8, 9, 10, 12, 13, 14, 16, 17, 18),in DAS-HFR3 (frequency reuse factor 3),x_(n) ^((i,F) ¹ ⁾=0,P_(n) ^((i,F) ¹ ⁾=0 when (n=1, 2, . . . , 6 and i=1,2, . . . , 7, 9, 11, 13, 15, 17),x_(n) ^((i,F) ² ⁾=0,P_(n) ^((i,F) ² ⁾=0 when (n=1, 2, . . . , 6 and i=0,2, 4, 6, 7, 8, 10, 11, 12, 14, 15, 16, 18),x_(n) ^((i,F) ³ ⁾=0,P_(n) ^((i,F) ³ ⁾=0 when (n=1, 2, . . . , 6 and i=0,1, 3, 5, 8, 9, 10, 12, 13, 14, 16, 17, 18),in DAS-FFR,x_(n) ^((i,f))≠0,P_(n) ^((i,f))≠0 when (n=0, 1, . . . , 6 and i=0, 1, .. . , 18, f=F₁, F₂, F₃),where P_(n) ^((i,f)) denotes the power constraint of the n-th DRU in thei-th cell for frequency band f.

The composite fading channel matrix H^((i,f)), i=0, 1, . . . , 18,encompasses not only small-scale fading (fast fading) but alsolarge-scale fading (slow fading), which is modeled as

$\begin{matrix}\begin{matrix}{H^{({i,f})} = {H_{w}^{({i,f})}L^{({i,f})}}} \\{= {{\left\lbrack {h_{0}^{({i,f})},h_{1}^{({i,f})},\ldots\mspace{14mu},h_{6}^{({i,f})}} \right\rbrack \cdot {diag}}\left\{ {l_{0}^{({i,f})},l_{1}^{({i,f})},\ldots\mspace{14mu},l_{6}^{({i,f})}} \right\}}}\end{matrix} & (3)\end{matrix}$where, H_(w) ^((i,f)) and L^((i,f)) reflect the small-scale channelfading and the large-scale channel fading between the DRUs in the i-thcell and the user in the central cell, respectively. {h_(j)^((i,f))|j=0, 1, . . . , 6; i=0, 1, . . . , 18; f=F₁, F₂, F₃} areindependent and identically distributed (i.i.d) circularly symmetriccomplex Gaussian variables with zero mean and unit variance, and {l_(n)^((i,f))|j=0, 1, . . . , 6; i=0, 1, . . . , 18; f=F₁, F₂, F₃} can bemodeled asl _(n) ^((i,f)) =√{square root over ([D_(n) ^((i))]^(−γ)χ_(n)^((i,f)))}, n=0, 1, . . . , 6, i=0, 1, . . . , 18  (4)Where D_(n) ^((i)) and χ_(n) ^((i,f)) are independent random variablesrepresenting the distance and the shadowing between the user in thecentral cell and the n-th DRU in the i-th cell, respectively. γ denotesthe path loss exponent. {χ_(j) ^((i,f))|j=0, 1, . . . , 6; i=0, 1, . . ., 18; f=F₁, F₂, F₃} are i.i.d random variables with probability densityfunction (PDF)

$\begin{matrix}{{{f_{\chi}(\chi)} = {\frac{1}{\sqrt{2\pi}{\lambda\sigma}_{\chi}\chi}{\exp\left( {- \frac{\left( {\ln\;\chi} \right)^{2}}{2\lambda^{2}\sigma_{\chi}^{2}}} \right)}}},{\chi > 0},} & (5)\end{matrix}$Where σ_(χ) is the shadowing standard deviation and

$\lambda = {\frac{\ln\; 10}{10}.}$

Since the number of interfering sources is sufficiently large andinterfering sources are independent with each other, the interferenceplus noise is assumed to be a complex Gaussian random vector as follows:

$\begin{matrix}{N^{(f)} = {{\sum\limits_{i = 1}^{18}{H^{({i,f})}x^{({i,f})}}} + n^{(f)}}} & (6)\end{matrix}$

The variance of N is derived by Central Limit Theorem as

$\begin{matrix}\begin{matrix}{{{Var}\left( N^{(f)} \right)} = {\left\lbrack {{\sum\limits_{i = 1}^{18}\;{\sum\limits_{n = 0}^{6}\;{\left\lbrack l_{n}^{({i,f})} \right\rbrack^{2}P_{n}^{({i,f})}}}} + \sigma_{n^{(f)}}^{2}} \right\rbrack I_{1}}} \\{= {\left\lbrack \sigma^{(f)} \right\rbrack^{2}I_{1}}}\end{matrix} & (7)\end{matrix}$Therefore, the received signal at the mobile station at a given symbolduration is given byy ^((0,f)) =H _(w) ^((0,f)) L ^((0,f)) x ^((0,f)) +N ^((f))  (8)

Dynamic Power Allocation

In DAS-SFR, it is important to dynamically change the frequency bandspower of each DRU to cope with a dynamically changing distribution oftraffic and to balance the throughput in each cell. Thus, it isnecessary to dynamically change the frequency bands power such that themaximum number of users in each cell could be satisfied (number of usersthat can achieve the targeted service bitrate). In this study we areinterested in a proper power allocation which maximizes the number ofsatisfied users and their capacity. Without proper power allocation,there may be cases of unbalanced capacity (throughput) where a few userscan have ultra-high throughput and most of the users have ultra-lowthroughput. In some cases, for the existence of very large interference,some users will be always unsatisfied. Therefore, a proper powerallocation can increase the throughput of the rest of the users.However, the number of unsatisfied users' throughput will be decreased.

III. Achievable Capacity of Distributed Antenna System

If we assume that the channel state information is known only at thereceiver (CSIR) and the channel is ergodic, the ergodic Shannon capacityat a given location of the target mobile station for the central cellcan be calculated by

$\begin{matrix}{C^{(f)} = {E_{H_{w}^{({0,f})}}\left\lbrack {\log_{2}{\det\left( {I_{1} + {\frac{1}{\left\lbrack \sigma^{(f)} \right\rbrack^{2}}\left( {H_{w}^{({0,f})}L^{({0,f})}} \right){P^{({0,f})}\left( {H_{w}^{({0,f})}L^{({0,f})}} \right)}^{H}}} \right)}} \right\rbrack}} & (9)\end{matrix}$where P^((0,f)) is the covariance matrix of the transmitted vector x andgiven by diag{P₀ ^((0,f)), P₁ ^((0,f)), . . . , P₆ ^((0,f))}. Ifergodicity of the channel is assumed, the ergodic capacity can beobtained as

$\begin{matrix}\begin{matrix}{C^{(f)} = {E_{H_{w}^{({0,f})}}\left\lbrack {\log_{2}\left( {1 + {\frac{1}{\left\lbrack \sigma^{(f)} \right\rbrack^{2}}{\sum\limits_{i = 0}^{6}\;{{{h_{i}^{({0,f})}}^{2}\left\lbrack l_{i}^{({0,f})} \right\rbrack}^{2}P_{i}^{({0,f})}}}}} \right)} \right\rbrack}} \\{= {\int_{\gamma_{f} = 0}^{\infty}{{\log_{2}\left( {1 + \gamma_{f}} \right)}{f_{\gamma_{f}}\left( \gamma_{f} \right)}\ {\mathbb{d}\gamma_{f}}}}}\end{matrix} & (10)\end{matrix}$where

$\gamma_{f} = {\frac{1}{\left\lbrack \sigma^{(f)} \right\rbrack^{2}}{\sum\limits_{i = 0}^{6}\;{{{h_{i}^{({0,f})}}^{2}\left\lbrack l_{i}^{({0,f})} \right\rbrack}^{2}P_{i}^{({0,f})}}}}$is a weighted chi-squared distributed random variable with p.d.f givenby

$\begin{matrix}{{{{f_{\gamma_{f}}\left( \gamma_{f} \right)}{\sum\limits_{i = 0}^{6}\;{\frac{\left\lbrack \sigma^{(f)} \right\rbrack^{2}\pi_{i}}{\left\lbrack l_{i}^{({0,f})} \right\rbrack^{2}P_{i}^{({0,f})}}{\exp\left( {- \frac{\left\lbrack \sigma^{(f)} \right\rbrack^{2}\gamma_{f}}{\left\lbrack l_{i}^{({0,f})} \right\rbrack^{2}P_{i}^{({0,f})}}} \right)}}}},{where}}{\pi_{i} = {\prod\limits_{{k = 0},{k \neq i}}^{6}\;{\frac{\left\lbrack l_{i}^{({0,f})} \right\rbrack^{2}P_{i}^{({0,f})}}{{\left\lbrack l_{i}^{({0,f})} \right\rbrack^{2}P_{i}^{({0,f})}} - {\left\lbrack l_{i}^{({0,f})} \right\rbrack^{2}P_{k}^{({0,f})}}}.}}}} & (11)\end{matrix}$

Then the ergodic capacity for MISO vector channel can be obtained in asimple form by [23]

$\begin{matrix}{{{{{MISO}\text{:}\mspace{14mu} C^{(f)}} = {{- \frac{1}{\ln\; 2}}{\sum\limits_{i = 0}^{6}\;{\pi_{i}{\exp\left( {- \frac{\left\lbrack \sigma^{(f)} \right\rbrack^{2}}{\left\lbrack l_{i}^{({0,f})} \right\rbrack^{2}P_{i}^{({0,f})}}} \right)}{{Ei}\left( {- \frac{\left\lbrack \sigma^{(f)} \right\rbrack^{2}}{\left\lbrack l_{i}^{({0,f})} \right\rbrack^{2}P_{i}^{({0,f})}}} \right)}}}}},\mspace{20mu}{f = F_{1}},F_{2},F_{3}}\;} & (12)\end{matrix}$where, Ei(t) is the exponential integral function

(Ei(t) = −∫_(−x)^(∞)𝕖^(−t)/t 𝕕t)and can be easily calculated with popular numerical tools such as MATLABand MAPLE.Since the derivation for this MISO vector channel is a generalization ofa SISO channel, the ergodic capacity for SISO channel is given,respectively, by

$\begin{matrix}{{{{{SISO}\text{:}\mspace{14mu} C^{(f)}} = {{- \frac{1}{\ln\; 2}}{\exp\left( {- \frac{\left\lbrack \sigma^{(f)} \right\rbrack^{2}}{\left\lbrack l_{0}^{({0,f})} \right\rbrack^{2}P_{0}^{({0,f})}}} \right)}{{Ei}\left( {- \frac{\left\lbrack \sigma^{(f)} \right\rbrack^{2}}{\left\lbrack l_{0}^{({0,f})} \right\rbrack^{2}P_{0}^{({0,f})}}} \right)}}},{f = F_{1}},F_{2},F_{3}}\;} & (13)\end{matrix}$

Hence, the total ergodic capacity of the system can be obtained byadding the capacity of the individual carriers,C _(total) =C ^((F) ¹ ⁾ +C ^((F) ² ⁾ +C ^((F) ³ ⁾  (14)where, for DAS-SFR at the central cell,

-   -   C^((F) ¹ ⁾: MISO, C^((F) ² ⁾: SISO, C^((F) ³ ⁾: SISO        for DAS-HFR3 (frequency reuse factor 3) at the central cell,    -   C^((F) ¹ ⁾: MISO, C^((F) ² ⁾: nothing, C^((F) ³ ⁾: nothing        for DAS-FFR at the central cell,    -   C^((F) ¹ ⁾: MISO, C^((F) ² ⁾: MISO, C^((F) ³ ⁾: MISO

In the following section, we present the analytical and numericalresults using a simulation to corroborate the theoretical analysis.

IV. Formulation of Power Allocation

In this section, we formulate the power allocation problem to maximizethe number of satisfied users and also maximize the total satisfiedusers capacity.

For the problem formulation we consider a service area with nineteencells shown in FIG. 2.

In a multiusers scenario, we can directly map the ergodic capacity ofeach user to what we obtained in section III depending on the positionand the power. Therefore, having a number of f resource blocks assignedto user k(N_(k) ^(RB(f))), the real throughput at user k can be writtenin terms of bps (bit per second) as follow,

$\begin{matrix}{{C_{k}^{real}(P)} = {W_{RB}{\sum\limits_{i = 1}^{3}\;{N_{k}^{{RB}{(F_{i})}} \cdot {C_{k}^{(F_{i})}(P)}}}}} & (15)\end{matrix}$where, W_(RB) is the resource block bandwidth. C_(k) ^((F) ¹ ⁾(P) is theergodic capacity of user k where P={P_(n) ^((i,f))|n=0, 1, . . . , 6,i=0, 1, . . . , 18, f=1, 2, 3}

We consider the following key performance indicators (KPIs) in the powerallocation system:

-   -   1. KPI_(SU) (Number of Satisfied Users): We can derive a metric        defining a percent of satisfied users (i.e., users that can        achieve the targeted service bit rate, for example, 1 Mbits/s).        The percent of satisfied users (out of m users) would be,

$\begin{matrix}{{{KPI}_{SU}(P)} = \frac{\sum\limits_{k = 1}^{m}\;{G_{k}(P)}}{N_{user}^{total}}} & (16)\end{matrix}$

-   -    where N_(user) ^(total) is total number of users and

${G_{k}(P)} = \left\{ \begin{matrix}1 & {{{when}\mspace{14mu}{C_{k}^{real}(P)}} > C_{th}} \\0 & {otherwise}\end{matrix} \right.$

Using these equations, C_(th) is a threshold capacity (targeted servicebit rate) and G_(k)(P) is unity when the capacity for a user (indexed byk) exceeds the threshold capacity and is equal to zero when the capacityis less than or equal to the threshold capacity.

-   -   2. KPI_(CSU) (Capacity of Satisfied Users): The total capacity        of satisfied users would be,

$\begin{matrix}{{{KPI}_{CSU}(P)} = \frac{\sum\limits_{k \in {SUS}}\;{C_{k}^{real}(P)}}{\left( {W_{(F_{1})} + W_{(F_{2})} + W_{(F_{3})}} \right)/3}} & (17)\end{matrix}$

-   -    where W^(f) is the bandwidth of frequency band f and        SUS={k|G_(k)=1, k=1, 2, . . . , m} is the satisfied users set.        If more than three carriers are utilized in a cell, the number        of carriers and the divisor in the denominator will increase as        appropriate.

Now, our QoS function is the weighted combination of the two KPIs (costfactors) which we have already introduced. Obviously our objectivefunction is to maximize the QoS function.

$\begin{matrix}{{\underset{P}{Maximize}\mspace{11mu}{{QoS}(P)}} = {{w_{1} \cdot {{KPI}_{SU}(P)}} + {w_{2} \cdot {{KPI}_{CSU}(P)}}}} & (18)\end{matrix}$

We can further simplify the objective functions in Eq. 18 based on thefollowing arguments:

Use round robin scheduling and equal bandwidth frequency for allfrequency bands, therefore, we can rewrite the real capacity in Eq. 15.as,

$\begin{matrix}\begin{matrix}{{C_{k}^{real}(P)} = {W_{RB}{\sum\limits_{i = 1}^{3}\;{N_{k}^{{RB}{(F_{i})}} \cdot {C_{k}^{(F_{i})}(P)}}}}} \\{{\overset{{Round}\mspace{14mu}{Robin}}{\longrightarrow}W_{RB}}{\sum\limits_{i = 1}^{3}\;{\frac{N_{RB}^{(F_{i})}}{N_{user}^{(F_{i})}}{C_{k}^{(F_{i})}(P)}}}} \\{\overset{{W_{RB}N_{RB}^{(F_{i})}} = W_{(F_{i})}}{\longrightarrow}{\sum\limits_{i = 1}^{3}\;{\frac{W_{(F_{i})}}{N_{user}^{(F_{i})}}{C_{k}^{(F_{i})}(P)}}}} \\{{\overset{W_{(F_{1})} = {W_{(F_{2})} = {W_{(F_{3})} = W_{F}}}}{\longrightarrow}W_{F}}{\sum\limits_{i = 1}^{3}\;\frac{C_{k}^{(F_{i})}(P)}{N_{user}^{(F_{i})}}}}\end{matrix} & (19)\end{matrix}$Where N_(user) ^((f)) is the number of users which can be supported byfrequency band f.

Since it is not practical to calculate the ergodic capacity for theindividual users, the aforementioned simplification is valid for thetheoretical analysis and cannot be extended to practical applications.However, in practice, the number of the satisfied users and thereforethe KPIs, are found based on the real users' throughput (C_(k)^(real)(P)) after the power allocation procedure.

Note that, the optimization problem variable (P) is 171=19×9, where thefirst term in the product is due to the fact that we have 19 cells, andthe second term is because each cell of DAS-SFR has 9 changeable userfrequency band powers. These 9 changeable user frequency band powers arecomprised of 6 frequency band powers for the edge DRUs and 3 frequencyband powers for central DRUs.

We decrease the optimization problem variable from 171 to 1 in such away that only the central DRU's frequency bands power, which are notassigned to the edge DRUs, are perturbed. The central DRU's F₂ and F₃power, which are not assigned to the edge DRUs, are perturbed for thecentral cell (eNB0) in a DAS-SFR configuration.

So the optimization problem is simplified to,

$\begin{matrix}{{\underset{\Delta\; P}{Maximize}\mspace{14mu}{{QoS}\left( {\Delta\; P} \right)}} = {{w_{1} \cdot {{KPI}_{SU}\left( {\Delta\; P} \right)}} + {w_{2} \cdot {{KPI}_{CSU}\left( {\Delta\; P} \right)}}}} & (20)\end{matrix}$where in DAS-SFR,

${\Delta\;{P\left( {d\; B} \right)}} = {{{P^{\prime}\left( {d\; B\; m} \right)} - {{P\left( {d\;{Bm}} \right)}\mspace{14mu} P_{n}^{({i,f})}}} = \left\{ \begin{matrix}P & {when} & \left( {{n = 0},1,\ldots\mspace{14mu},6} \right. & {and} & {{i = 0},8,10,12,14,16,18} & {and} & \left. {f = F_{1}} \right) & {or} \\\; & \; & \left( {{n = 0},1,\ldots\mspace{14mu},6} \right. & {and} & {{i = 1},3,5,9,13,17} & {and} & \left. {f = F_{2}} \right) & {or} \\\; & \; & \left( {{n = 0},1,\ldots\mspace{14mu},6} \right. & {and} & {{i = 2},4,6,7,11,15} & {and} & {\left. {f = F_{3}} \right),} & \; \\P^{\prime} & {when} & \left( {n = 0} \right. & {and} & {{i = 1},2,\ldots\mspace{14mu},7,9,11,13,15,17} & {and} & \left. {f = F_{1}} \right) & {or} \\\; & \; & \left( {n = 0} \right. & {and} & {{i = 0},2,4,6,7,8,10,} & {and} & \left. {f = F_{2}} \right) & {or} \\\; & \; & \; & \; & {11,12,14,15,16,18} & \; & \; & \; \\\; & \; & \left( {n = 0} \right. & {and} & {{i = 0},1,3,5,8,9,10,} & {and} & {\left. {f = F_{3}} \right),} & \; \\\; & \; & \; & \; & {12,13,14,16,17,18} & \; & \; & \; \\0 & {otherwise} & \; & \; & \; & \; & \; & \;\end{matrix} \right.}$

${{KPI}_{SU}\left( {\Delta\; P} \right)} = {\frac{\sum\limits_{k = 1}^{m}\;{G_{k}\left( {\Delta\; P} \right)}}{N_{user}^{total}}\mspace{14mu}{where}}$${G_{k}\left( {\Delta\; P} \right)} = \left\{ {{\begin{matrix}1 & {{{when}\mspace{14mu}{\sum\limits_{i = 1}^{3}\;\frac{C_{k}^{(F_{i})}\left( {\Delta\; P} \right)}{N_{user}^{(F_{i})}}}} > \frac{C_{th}}{W_{F}}} \\0 & {{otherwise},}\end{matrix}{{KPI}_{CSU}\left( {\Delta\; P} \right)}} = {\sum\limits_{k \in {SUS}}\;{\sum\limits_{i = 1}^{3}\;\frac{C_{k}^{(F_{i})}\left( {\Delta\; P} \right)}{N_{user}^{(F_{i})}}}}} \right.$

In our analysis, we assume that P is fixed and only P′ changes inmagnitude.

In multiuser systems, we need to consider the different resourceallocation scenarios which were defined in section II. B

In LTE systems, eNB distinguishes between the interior and the exteriorusers based on their corresponding uplink power received at the centralDRU. Particularly in DAS-SFR, since none of the DRUs except the centralDRU operates in F₂ and F₃, it is possible to apply the above-mentionedmethod (distinguishing between the interior and the exterior users)using the received CQIs (Channel Quality Indicator) from F₂ and F₃. Toimplement these techniques, we propose a threshold T_(p) as a parameterin the eNB such that users with uplink power higher than T_(p) areassigned as interior users, and vice versa. In a DAS-SFR, T_(p) can playthe same role as a threshold for CQI such that users with CQI higherthan T_(p) are assigned as interior users, and vice versa.

A. The Power Self-Optimization Algorithm

According to the above intuitive analysis, we propose a powerself-optimization (PSO) technique which is based on a simple anddecentralized algorithm that runs on the application layer.

In the PSO algorithm, the expected network gain, which is based on oneor both system KPIs, is used in order to determine whether to increaseor decrease the transmission power of the central DRUs. To do so, thePSO technique uses the KPI associated with each eNB to compute thesystem KPI. Finally, the central DRUs are in charge of adjusting ΔPbased on system KPI by performing the PSO algorithm. FIG. 4 depicts theblock diagram of the self-optimization algorithm. As illustrated in FIG.4, both KPIs are functions of ΔP.

Observing the block diagram shown in FIG. 4, it is possible to note thatthe transmission power is adjusted by comparing the current KPI,calculated at the end of current phase, and the last KPI, calculated atthe end of last phase. Moreover, it is important to highlight that thecentral DRUs have a predefined minimum and maximum transmission power(p^(min) and p^(max)), which cannot be exceeded by the algorithm. Thus,the self-optimization algorithm increases or decreases the ΔPstep-by-step by p (dB) for each central DRUs. Parameter t can take twovalues, 1 and −1, where 1 shows that algorithm starts by increasing thepower level. Conversely, −1 indicates that the algorithm starts bydecreasing the power level. Since we do not want the power to oscillatearound the optimal power forever, we define the parameter c to help thealgorithm stop.

Whenever the algorithm starts off by increasing the power level, thecentral DRUs increase the ΔP by the fixed parameter p. The central DRUkeep increasing the power by the fixed parameters p as long as thecurrent calculated KPI_(SU) is greater than the last calculatedKPI_(SU). If the current calculated KPI_(SU) is equal to last calculatedKPI_(SU), the central DRUs keep increasing the power as long as thecurrent calculated KPI_(CSU) is not smaller than the last calculatedKPI_(CSU), otherwise it decreases its power level. Note that wheneverthe algorithm starts off by increasing the power level, all the abovementioned statements should be reversed i.e. the decreasing behaviorshould be changed to an increasing behavior and vice versa.

The PSO algorithm seeks to maximize the number of satisfied usersmeanwhile it seeks to maximize the capacity of the satisfied users inorder to have a better QoS. Even though some embodiments do not achievean optimal solution, the methods described herein provide stable powerupdates toward the optimal solution. In other embodiments, the optimalsolution is obtained.

Referring to FIG. 4, KPI_(SU) is the Key Performance Indicator forSatisfied Users and KPI_(CSU) is the key performance indicator for theCapacity of Satisfied Users. ΔP is the change in power of the carriers.By adjusting the power of the carriers, the number of satisfied usersand the capacity of the satisfied users can be increased or optimized.Initially, t is set to 1, c is set to zero, ΔP=0, and p=1 (i.e., thepower increments are made in 1 dBm steps). In the illustratedembodiment, the maximum and minimum values of power (measured in dBm inan embodiment) are 20 and −10, respectively. In some implementations,the maximum and minimum power are set by the user and the valuesprovided herein are merely given by way of example. Thus, depending onthe system parameters, different values will be utilized for the maximumand minimum power. One of ordinary skill in the art would recognize manyvariations, modifications, and alternatives.

A measurement of the KPI_(SU) given ΔP (initially zero, for which thepower of the various carriers is equal) is made and the result isassigned to KPI*_(SU). Thus, the performance for the users in a givencell is measured to determine the number of satisfied users in the cell.The capacity for the satisfied users is also measured at this value ofΔP (KPI_(CSU) given ΔP) and assigned to KPI*_(CSU).

The difference in power is then modified (ΔP+(t*p)) in order to iterateon the difference in power. t is an updating index that has values ofpositive or negative one, indicating if the difference in power is beingincreased or decreased. Referring to FIG. 4, movement through the lefthand side of the loop results in increases in power and movement throughthe right hand side of the loop results in decreases in power.

In order to determine if the power is in the correct range, a comparisonis made between ΔP and the maximum power (ΔP>p^(max)), between ΔP andthe minimum power (ΔP <p^(min), and that an oscillation indicator (c) isnot reached. If any of these conditions are true, then the method isterminated. Otherwise, if the power is within the predetermined range(less than maximum power and greater than the minimum power) andoscillation has not been detected, the method continues.

A measurement is made of the number of satisfied users given the new ΔP(KPI_(SU)(ΔP )) and this measured value is compared to the previousnumber of satisfied users. If the change in power (an increase in thisexample) has resulted in a decrease in the number of satisfied users,then the right hand loop is used to toggle the updating index (t), whichwill enable the power to be decreased in the subsequent flow.

If, on the other hand, the number of satisfied users given the new ΔP isgreater than or equal to the previous number of satisfied users,indicating no change or an increase in the number of satisfied users,the method proceeds to the next comparison to determine if the number ofsatisfied users given the new ΔP is equal to the previous number ofsatisfied users. If the comparison is not equal, then the left hand sideof the loop is used to increase the power differential in the subsequentflow.

If the number of satisfied users given the new ΔP is equal to theprevious number of satisfied users, then a measurement is made of thecapacity of the satisfied users and this value is compared to theprevious capacity. If the measured capacity is less than the previouscapacity, the right hand side of the loop is used to decrease the powerdifferential in the subsequent flow. If the measured capacity is greaterthan or equal to the previous capacity, then the left hand side of theloop is used to increase the power differential in the subsequent flow.

Referring to FIG. 1, the method illustrated in FIG. 4 will be applied inrelation to the carriers used in the central antenna (eNB0) of the cell(i.e., hexagon). For each cell, the carrier used in the peripheralportions of the cell will be used as a reference and the other carrierswill have their power set by optimizing the number and capacity ofsatisfied users using the algorithm described herein. In someembodiments, the carriers used in the central antenna that are not usedin the peripheral portions of the cell will have the same power,providing a single ΔP for the central antenna with the carrier used inthe peripheral portions of the cell providing the reference. In someimplementations, the carriers used only in the central antenna can havediffering powers with the algorithm applied to the carriers individually(e.g., F₁ compared to F₃ and F₂ compared to F₃ for the rightmost cell inFIG. 1A).

Referring to FIG. 1A, F₁ is the reference for the top left cell, F₂ isthe reference for the bottom left cell, and F₃ is the reference for therightmost cell. One of ordinary skill in the art would recognize manyvariations, modifications, and alternatives. Embodiments of the presentinvention provide methods and systems in which the number of carriers ina cell can be increased, thereby increasing bandwidth. The algorithm isthen used to set the power level of the added carriers to a level thatreduced interference with adjacent cells to an acceptable level.

It should be appreciated that the specific steps illustrated in FIG. 4provide a particular method of increasing a number and capacity ofsatisfied users by varying power between carriers according to anembodiment of the present invention. Other sequences of steps may alsobe performed according to alternative embodiments. For example,alternative embodiments of the present invention may perform the stepsoutlined above in a different order. Moreover, the individual stepsillustrated in FIG. 4 may include multiple sub-steps that may beperformed in various sequences as appropriate to the individual step.Furthermore, additional steps may be added or removed depending on theparticular applications. One of ordinary skill in the art wouldrecognize many variations, modifications, and alternatives.

V. Analytical and Simulation Results

FIG. 5 represents the ergodic capacity of a cellular DAS's central cellfor different frequency reuse techniques versus the normalized distancefrom the eNB0 DRU0 in the direction of the worst case position X, for apath loss exponent of 3.76. Each scenario is plotted for the individualcapacities C^((F) ¹ ⁾, C^((F) ² ⁾, C^((F) ³ ⁾ and also for the totalcapacity C_(total). These figures show an interesting non-monotonicrelationship between capacity and the normalized distance from the basestation. This is due to the fact that the signal from a distributedantenna module becomes dominant around 0.6R.

As it can be observed in FIG. 5, when applying the SFR methods, byincreasing ΔP from −10 dB to 20 dB, the central cell's C^((F) ² ⁾ andC^((F) ³ ⁾ increase. This, however, increases the interferenceassociated with the edge DAUs of the neighboring cells which are usingF₂ and F₃ as their main frequency band. It is necessary to note that,increasing ΔP from −10 dB to 20 dB, significantly increases theassociated interference with the F₁ frequency band in the central cell,imposed from the neighboring cells, and thus decreases the centralcell's C^((F) ¹ ⁾.

It is important to notice that, considering SFR methods, as powerincreases, C_(total) does not change harmonically, which means theergodic capacity associated with the cell's interior regions increases,and that of the cell's exterior regions decreases. Therefore, the users'distribution within the cell's area plays a significant role whendeciding the optimal ΔP.

A secondary consideration when deciding the optimal ΔP is the minimumrequired capacity (C_(th)). As an example, with a high C_(th) (ergodiccapacity=20 bit/Hz in FIG. 5), as ΔP increases, a wider radiance in acell will be covered by ergodic capacity higher than 20. With a lowC_(th) (ergodic capacity=3 bit/Hz in FIG. 5), as ΔP increases, a shorterradiance in the cells will be covered by ergodic capacity higher than 3.

The FFR method fully uses the frequency bands, therefore, the cell'sinterior regions' achieved an ergodic capacity higher than ergodiccapacity in the cell's interior regions when applying the HFR3 method.For example, at ergodic capacity=20, the FFR method outperforms the HFR3method, considering the users' satisfaction probability. However, whenapplying the FFR method, due to the interference caused by theneighboring cells, the edge cells frequently experience dead spots. Asan example, considering the users' satisfaction probability, for ergodiccapacity=3, the HFR3 method outperforms the FFR method.

FIGS. 6 and 7 demonstrate the two KPI_(SU) and KPI_(CSU) for differentΔP, considering four different user distributions. The only parameterthat is different in the aforementioned figures is their C_(th), i.e. weconsider low C_(th)=0.01W_(RB) and high C_(th)=0.07W_(RB), in FIGS. 6and 7, respectively. In theoretical analysis, the interior region isdistinguished from the exterior region, based on T_(p). In other words,the region with ergodic capacity higher than T_(p) is considered asinterior region, and the region with ergodic capacity lower than T_(p)is considered as exterior region. This T_(p) is associated to theregion's ergodic capacity of the frequency bands that are only allocatedto the central DRUs. We assume T_(p)=2 (bit/Hz) in our theoreticalanalyses.

Since both KPI functions are dependent on G_(k), it is reasonable toconsider each of these functions as a criteria to measure the QoS. Weanalyze two different cases, i.e. (w₁=1, w₂=0) and (w₁=0, w₂=1). In thefirst case, we presume KPI_(SU) as our QoS function whereas in thesecond case we consider KPI_(CSU) as our QoS function.

We define our user distributions as depicted in Table 1. where

$\mspace{11mu}{{N_{user}^{total} = {\sum\limits_{i}\;{X_{i}S_{i}}}},}$iε{region A, region B, region C, region D}, S_(i) is the area of regioni and X_(i)=(# users of region i)/S_(i). We perform Monte Carlosimulations to corroborate the analytical results. It is assumed thatthe total number of users (N_(user) ^(total)) is 200.

As it is seen in FIG. 6, when C_(th) takes a low value, i.e. C_(th)=0.01W_(RB), except for the HFR1 method, applying the rest of the frequencyreuse methods (FFR, HFR3, SFR) results in the highest number of thesatisfied users (KPI_(SU)). Note that, as ΔP increases, when applyingDAS-SFR, the number of the satisfied users asymptotically decreases. Theabove mentioned results hold for all 4 different user distributions.

As was shown in FIG. 6, there exists an optimal ΔP at which theKPI_(CSU) is maximum, for all four different distributions. Forinstance, when applying the DAS-SFR-Scenario3 method, for the UD, DCD,DCED and DED, the maximum KPI_(CSU) happens at ΔP=−5 dB, 2 dB, 8 dB, and−4 dB, respectively.

One has to consider, the optimal ΔP is different for dissimilardistribution scenarios. Moreover, the DAS-SFR-Scenario3 methodoutperforms the other two DAS-SFR methods, for all the distributionsunder consideration.

FIG. 7 reveals that, when C_(th) takes a large value, i.e.C_(th)=0.07W_(RB), the HRF1 method outperforms the HFR3 method,considering the number of the satisfied users (KPI_(SU)). Thiscorroborates our analytical results from FIG. 5, as it was explainedpreviously. However, the DAS-SFR-Scenario2 method outperforms all theother methods, at different optimal ΔP values for dissimilardistribution scenarios.

As it can be perceived from FIG. 7, there exists an optimal ΔP at whichthe KPI_(SU) and KPI_(CSU) are maximum, for all four differentdistributions. As an example, when applying the DAS-SFR-Scenario2method, for the UD, DCD, DCED and DED, the maximum KPI_(SU) andKPI_(CSU) happen at ΔP=6 dB, 4 dB, −2 dB, and 13 dB, respectively.

Note that, the optimal ΔP is different for different distributionscenarios. Moreover, the DAS-SFR-Scenario2 method outperforms the othertwo SFR methods, for all distributions under consideration. Since theDAS-SFR-Scenario2 uses all the frequency bands in the interior cellregion, along with the fact that the users with throughput above theC_(th) are mainly located in the interior cell region, leads to thefinal conclusion that DAS-SFR-Scenario2 outperforms the other methods.

The capacity of the above mentioned architectures is also investigatedthrough system level simulations. We consider the two-ring hexagonalcellular system with nineteen eNBs, such that each cell has 7 DRUs, asdepicted in FIG. 2, where the eNBs distance is 500 meters. The 200 UEsare distributed for 4 user distribution methods which are defined inTable 1. An eNB allocates the available RBs to UEs by estimating thesignaling and uplink power of UEs. We use the simulation parameterslisted in Table 2.

At a TTI (Transmission Time Interval) for the simulation, the eNB in acell gathers the CQI (Channel Quality Indicator) information of UEs andallocates the RBs to each UE, using the Round Robin schedulingtechnique. The throughput of a UE is obtained based on the SINR of theUE in the assigned RB. In system level simulation, SINR is determined bythe path loss and lognormal fading measured in RB. The throughput of aUE is estimated using the Shannon capacity as followsC _(m) ^((f)) =W _(RB) _((f)) log(1+SINR_(m) ^((f))), f=F ₁ , F ₂ , F₃  (21)where, W_(RB) _((f)) is the bandwidth of RBs assigned to a UE andSINR_(m) ^((f)) is the SINR of a UE_(m). The cell capacity in eachregion is the total throughput of UEs in the corresponding region and isexpressed as follows

$\begin{matrix}{C_{total} = {\sum\limits_{i = 1}^{3}\;{\sum\limits_{m = 1}^{M}\; C_{m}^{(F_{i})}}}} & (22)\end{matrix}$Where M is the number of UEs in a group.The presented numerical results corroborate the analytical resultsdepicted in FIG. 6 and FIG. 7.

Embodiments of the present invention provide a new cell architecturecombining two inter-cell interference mitigation techniques, DistributedAntenna System and Soft Frequency Reuse, to improve cell edge user'sthroughput when the system has full spectral efficiency. A powerself-optimization algorithm that aims at maximizing the number ofsatisfied users while trying to increase their capacity was alsoproposed. In more detail, the self-optimization algorithm uses the KPIscomputed by the server in the last phase and current phase to adjust thepower level for the next phase.

An analytical framework is derived to evaluate the user throughputleading to tractable expressions. A natural extension of this work is toaddress the cellular uplink. The overall capacity increases by using theSFR technique, since the spectral efficiency in the interior region ishigher than that in the exterior region when compared to HFR3 technique.The cell edge user's throughput increases by using the SFR technique;since the interference signal from neighbor cells is lower than that thetime we use FFR technique.

Analytical and simulation results demonstrated the advantage of usingthe self-optimization algorithm instead of setting a fixed power level.When a DAS-SFR without the PSO algorithm is considered, the transmissionpower is set at the beginning of the communication and remains the sameduring its entire network lifetime. This characteristic can be negativeconsidering a DAS-SFR in a real environment where the inherent userdistribution is not constant.

Due to the fact that the inherent environment user distribution iscompletely variable, the PSO algorithm always guarantees the maximumnumber of satisfied users during the communication, while the algorithmserves to maximize their capacity as well.

TABLE 1 X_(i)/n, iε{A,B,C,D} R₁ R₂ UD⁽¹⁾ DCD⁽²⁾ DCED⁽³⁾ DED⁽⁴⁾ Region A0 0.25 1 7 1 1 Region B 0.25 0.50 1 1 7 1 Region C 0.50 0.75 1 1 1 1Region D 0.75 1 1 1 1 7 ⁽¹⁾UD: Uniform Distribution ⁽²⁾DCD: Dense at theCenter Distribution ⁽³⁾DCED: Dense at the mid. of Cent. And Edge cellDistribution ⁽⁴⁾DED: Dense at the Edge cell Distribution

TABLE 2 Simulation Parameters PARAMETERS VALUE Channel Bandwidth foreach 5 MHz Frequency Part Carrier Frequency 2.14 GHz FFT size 1024Number of Resource Blocks 25 for each Frequency Part Subcarrier Spacing15 kHz Cellular Layout Hexagonal grid, 19 sites Inter-eNB Distance 500meters Log-normal Shadowing 8 dB Propagation loss 128.1 + 37.6log₁₀(R(km)) White Noise Power Density −174 dBm/Hz Scheduling RoundRobin TTI 1 ms T_(p) (CQI) 2 CQI

What is claimed is:
 1. A method of allocating transmission power in acommunications system including a processor, the method comprising: a)setting a power differential for an antenna in a cell of thecommunication system, the power differential being a difference betweena transmission power of one or more carriers and a transmission power ofa reference carrier; b) measuring a percentage of satisfied users at thepower differential, wherein a satisfied user is defined as a user havinga capacity above a predetermined threshold capacity; c) measuring atotal capacity for the satisfied users at the power differential; d)adjusting the power differential by a predetermined amount by increasingor decreasing the transmission power of the one or more carriers; e)measuring an updated percentage of satisfied users at the adjusted powerdifferential; f) determining, using the processor, that the updatedpercentage of satisfied users is greater than or equal to the percentageof satisfied users at the power differential; and g) repeating a)-f) toobtain an iterated power level; and h) setting the transmission power ofthe one or more carriers at the iterated power level.
 2. The method ofclaim 1 wherein the reference carrier comprises a first frequencycarrier, and the one or more carriers comprise a second frequencycarrier and a third frequency carrier.
 3. The method of claim 1 whereinthe reference carrier is utilized by multiple antennas in the cell ofthe communications system and the one or more carriers are utilized by asingle antenna in the cell of the communications system.
 4. The methodof claim 1 wherein the predetermined threshold capacity is defined by apredetermined threshold bit rate.
 5. The method of claim 1 furthercomprising: determining that the adjusted power differential is outsidea predetermined range; and terminating the method.
 6. The method ofclaim 1 further comprising: determining that an oscillation indicator isequal to a predetermined value; and terminating the method.
 7. Themethod of claim 1 further comprising measuring an updated total capacityfor the satisfied users at the adjusted power differential, anddetermining, using the processor, that the updated total capacity forthe satisfied users at the adjusted power differential is less than thetotal capacity for the satisfied users at the power differential.
 8. Themethod of claim 3 wherein the single antenna is the antenna, and theantenna is at a center of the cell.
 9. The method of claim 8 wherein themultiple antennas are at an edge of the cell.
 10. The method of claim 9wherein the multiple antennas comprise six antennas.